1: This document discusses linear regression analysis in R, including preparing data, specifying models, and interpreting results. 2: Key steps covered include recoding and transforming variables, specifying linear regression models using formula syntax, fitting models using lm(), and interpreting model outputs like coefficients, confidence intervals, and ANOVA tables. 3: Interactions are discussed, along with visualizing effects using the effects package. Both type I and type III ANOVA tables are demonstrated along with distinguishing their interpretations.

1. Linear Regression
with
1: Prepare data/specify model/read results
2012-12-07 @HSPH
Kazuki Yoshida, M.D.
MPH-CLE student
FREEDOM
TO
KNOW

2. Group Website is at:
http://rpubs.com/kaz_yos/useR_at_HSPH

3. Previously in this group
n Introduction n Graphics
n Reading Data into R (1) n Groupwise, continuous
n Reading Data into R (2) n
n Descriptive, continuous
n Descriptive, categorical
n Deducer

4. Menu
n Linear regression

5. Ingredients
Statistics Programming
n Data preparation n within()
n Model formula n factor(), relevel()
n lm()
n formula = Y ~ X1 + X2
n summary()
n anova(), car::Anova()

6. Open
R Studio

7. Create a new script
and save it.

8. http://www.umass.edu/statdata/statdata/data/

9. We will use lowbwt dataset used in BIO213
lowbwt.dat
http://www.umass.edu/statdata/statdata/data/lowbwt.txt
http://www.umass.edu/statdata/statdata/data/lowbwt.dat

10. Load dataset from web
lbw <- read.table("http://www.umass.edu/statdata/statdata/data/lowbwt.dat",
head = T, skip = 4)
skip 4 rows
header = TRUE
to pick up
variable names

11. “Fix” dataset
lbw[c(10,39), "BWT"] <- c(2655, 3035)
BWT column
Replace data points
10th,39th to make the dataset identical
rows to BIO213 dataset

12. Lower case variable names
names(lbw) <- tolower(names(lbw))
Put them back into Convert variable
variable names names to lower case

13. See overview

14. library(gpairs)
gpairs(lbw)

16. Recoding
Changing and creating variables

17. Name of newly created dataset
(here replacing original) Take dataset
dataset <-
within(dataset, {
_variable manipulations_
}) Perform variable manipulation
You can specify by variable name
only. No need for dataset$var_name

18. lbw <- within(lbw, {
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
## Categorize ftv (frequency of visit)
ftv.cat <- cut(ftv, breaks = c(-Inf, 0, 2, Inf), labels = c("None","Normal","Many"))
ftv.cat <- relevel(ftv.cat, ref = "Normal")
## Dichotomize ptl
preterm <- factor(ptl >= 1, levels = c(F,T), labels = c("0","1+"))
})

19. Numeric to categorical:
element by element 1st will be reference
lbw <- within(lbw, {
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
## Categorize ftv (frequency of visit)
ftv.cat <- cut(ftv, breaks = c(-Inf, 0, 2, Inf), labels = c("None","Normal","Many"))
ftv.cat <- relevel(ftv.cat, ref = "Normal")
## Dichotomize ptl
preterm <- factor(ptl >= 1, levels = c(F,T), labels = c("0","1+"))
})
1 to White 1st will be reference
Categorize race and label: 2 to Black
3 to Other

20. Explained more in depth
factor() to create categorical variable
Create new
variable named Take race variable
race.cat
lbw <- within(lbw, {
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
})
Order levels 1, 2, 3
Make 1 reference level
Label levels 1, 2, 3 as
White, Black, Other

21. Numeric to categorical:
range to element
lbw <- within(lbw, {
1st will be reference
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
## Categorize ftv (frequency of visit)
ftv.cat <- cut(ftv, breaks = c(-Inf, 0, 2, Inf), labels = c("None","Normal","Many"))
ftv.cat <- relevel(ftv.cat, ref = "Normal")
## Dichotomize ptl
preterm <- factor(ptl >= 1, levels = c(F,T), labels = c("0","1+"))
}) How breaks work
(-Inf 0] 1 2] 3 4 5 6 Inf ]
None Normal Many

22. Reset reference level
lbw <- within(lbw, {
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
## Categorize ftv (frequency of visit)
ftv.cat <- cut(ftv, breaks = c(-Inf, 0, 2, Inf), labels = c("None","Normal","Many"))
ftv.cat <- relevel(ftv.cat, ref = "Normal")
## Dichotomize ptl
preterm <- factor(ptl >= 1, levels = c(F,T), labels = c("0","1+"))
})
Change reference level of ftv.cat variable
from None to Normal

23. Numeric to Boolean to Category
lbw <- within(lbw, {
## Relabel race
race.cat <- factor(race, levels = 1:3, labels = c("White","Black","Other"))
## Categorize ftv (frequency of visit)
ftv.cat <- cut(ftv, breaks = c(-Inf, 0, 2, Inf), labels = c("None","Normal","Many"))
ftv.cat <- relevel(ftv.cat, ref = "Normal")
## Dichotomize ptl
preterm <- factor(ptl >= 1, levels = c(FALSE,TRUE), labels = c("0","1+"))
})
TRUE, FALSE ptl < 1 to FALSE, then to “0”
vector created ptl >= 1 to TRUE, then to “1+”
here levels labels

24. Binary 0,1 to No,Yes
lbw <- within(lbw, {
## Categorize smoke ht ui
smoke <- factor(smoke, levels = 0:1, labels = c("No","Yes")) One-by-one
ht <- factor(ht, levels = 0:1, labels = c("No","Yes"))
ui <- factor(ui, levels = 0:1, labels = c("No","Yes")) method
})
## Alternative to above
lbw[,c("smoke","ht","ui")] <-
lapply(lbw[,c("smoke","ht","ui")],
function(var) { Loop method
var <- factor(var, levels = 0:1, labels = c("No","Yes"))
})

25. model formula

26. formula
outcome ~ predictor1 + predictor2 + predictor3
SAS equivalent:
model outcome = predictor1 predictor2 predictor3;

27. In the case of t-test
continuous variable grouping variable to
to be compared separate groups
age ~ zyg
Variable to be Variable used
explained to explain

28. linear sum
Y ~ X1 + X2

29. n . All variables except for the outcome
n + X2 Add X2 term
n - 1 Remove intercept
n X1:X2 Interaction term between X1 and X2
n X1*X2 Main effects and interaction term

30. Interaction term
Y ~ X1 + X2 + X1:X2
Main effects Interaction

31. Interaction term
Y ~ X1 * X2
Main effects & interaction

32. On-the-fly variable manipulation
Inhibit formula
interpretation. For math
manipulation
Y ~ X1 + I(X2 * X3)
New variable (X2 times X3)
created on-the-fly and used

33. Fit a model
lm.full <- lm(bwt ~ age + lwt + smoke + ht + ui +
ftv.cat + race.cat + preterm ,
data = lbw)

34. See model object
lm.full

35. Call: command repeated
Coefficient for each
variable

36. See summary
summary(lm.full)

37. Call: command repeated Residual
distribution
Coef/SE = t
Dummy
variables
created
Model R^2 and adjusted R^2
F-test

38. ftv.catNone No 1st trimester visit people compared to
Normal 1st trimester visit people (reference level)
ftv.catMany Many 1st trimester visit people compared to
Normal 1st trimester visit people (reference level)

39. race.catBlack Black people compared to
White people (reference level)
race.catOther Other people compared to
White people (reference level)

40. Confidence intervals
confint(fit.lm)

41. Confidence intervals
Lower Upper
boundary boundary

42. ANOVA table (type I)
anova(lm.full)

43. ANOVA table (type I)
degree of Sequential Mean SS
freedom SS = SS/DF
F = Mean SS / Mean SS of residual

44. Type I = Sequential SS
1 age
1st gets all in type I
er lap
ov I
ut pe
ll b n ty
sa 1i
las et n
g e 2 lwt
on emtr nd twe
2 e
ly b
in aini
typ ng
3 smoke eI

45. ANOVA table (type III)
library(car)
Anova(lm.full, type = 3)

46. ANOVA table (type III)
Marginal degree of
SS freedom
Multi-
category
variables
tested as
one
F = Mean SS / Mean SS of residual

47. Type III = Marginal SS
1 age
gin
ar I
ets m e II
1s t g typ
in
o nly
e I in
typ rg
II
i n ma
las
ly ets
on tg 2 lwt
ets
dg
ly
in ma
2n
typ rg
on
3 smoke e I in
II

48. Comparison
Type I Type III

49. Effect plot
library(effects)
plot(allEffects(lm.full), ylim = c(2000,4000))
Fix Y-axis
values for all
plots

50. Effect of a variable
with other covariate
set at average

51. Interaction

52. This model is for
demonstration purpose.
Continuous * Continuous
lm.full.int <- lm(bwt ~ age*lwt + smoke +
ht + ui + age*ftv.cat + race.cat*preterm,
data = lbw)
Continuous * Categorical
Categorical * Categorical

53. Anova(lm.full.int, type = 3)

54. Marginal degree of
SS freedom
Interaction
terms
F = Mean SS / Mean SS of residual

55. plot(effect("age:lwt", lm.full.int))
lwt level
Continuous * Continuous

56. plot(effect("age:ftv.cat", lm.full.int), multiline = TRUE)
Continuous * Categorical

57. plot(effect(c("race.cat*preterm"), lm.full.int),
x.var = "preterm", z.var = "race.cat", multiline = TRUE)
Categorical * Categorical